Question: Solve for $x$ and $y$ using elimination. ${2x+3y = 8}$ ${-2x+4y = 6}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $7y = 14$ $\dfrac{7y}{{7}} = \dfrac{14}{{7}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {2x+3y = 8}\thinspace$ to find $x$ ${2x + 3}{(2)}{= 8}$ $2x+6 = 8$ $2x+6{-6} = 8{-6}$ $2x = 2$ $\dfrac{2x}{{2}} = \dfrac{2}{{2}}$ ${x = 1}$ You can also plug ${y = 2}$ into $\thinspace {-2x+4y = 6}\thinspace$ and get the same answer for $x$ : ${-2x + 4}{(2)}{= 6}$ ${x = 1}$